2022/09/08 by Lorenzo La Porta, La Porta, Lorenzo
Mathematics · #11G18 (Primary) 11G25 #14G17 #14G35 #14K10 (Secondary) #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2209.03717
openalex publication_date 2022/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main result of this paper is the construction of a new class of weight shifting operators, similar to the theta operators of arXiv:1902.10911, arXiv:1712.06969 and others, which are defined on the lower Ekedahl-Oort strata of the geometric special fibre of unitary Shimura varieties of signature (n-1, 1) at a good prime p, split in the in the reflex field E, which we assume to be quadratic imaginary. These operators act on certain graded sheaves which are obtained from the arithmetic structure of the EO strata, in particular the p-rank on each stratum. We expect these operators to have applications to the study of Hecke-eigensystems of modular forms modulo p and generalisations of the weight part of Serre's conjecture.